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Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result

Bellan, P. M. (2003) Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result. Physics of Plasmas, 10 (5). pp. 1999-2008. ISSN 1070-664X.

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Suppose an electric current I flows along a magnetic flux tube that has poloidal flux psi and radius a = a(z), where z is the axial position along the flux tube. This current creates a toroidal magnetic field Bphi. It is shown that, in such a case, nonlinear, nonconservative J×B forces accelerate plasma axially from regions of small a to regions of large a and that this acceleration is proportional to [partial-derivative]I2/[partial-derivative]z. Thus, if a current-carrying flux tube is bulged at, say, z = 0 and constricted at, say, z = ±h, then plasma will be accelerated from z = ±h towards z = 0 resulting in a situation similar to two water jets pointed at each other. The ingested plasma convects embedded, frozen-in toroidal magnetic flux from z = ±h to z = 0. The counterdirected flows collide and stagnate at z = 0 and in so doing (i) convert their translational kinetic energy into heat, (ii) increase the plasma density at z[approximate]0, and (iii) increase the embedded toroidal flux density at z[approximate]0. The increase in toroidal flux density at z[approximate]0 increases Bphi and hence increases the magnetic pinch force at z[approximate]0 and so causes a reduction of a(0). Thus, the flux tube develops an axially uniform cross section, a decreased volume, an increased density, and an increased temperature. This model is proposed as a likely hypothesis for the long-standing mystery of why solar coronal loops are observed to be axially uniform, hot, and bright. It is furthermore argued that a small number of tail particles bouncing between the approaching counterstreaming plasma jets should be Fermi accelerated to extreme energies. Finally, analytic solution of the Grad–Shafranov equation predicts that a flux tube becomes axially uniform when the ingested plasma becomes hot and dense enough to have 2µ0nkappaT/B<sub>pol</sub><sup>2</sup> = (µ0Ia(0)/psi)2/2; observed coronal loop parameters are in reasonable agreement with this relationship which is analogous to having betapol = 1 in a tokamak.

Item Type:Article
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URLURL TypeDescription Paper
Bellan, P. M.0000-0002-0886-8782
Additional Information:© 2003 American Institute of Physics. (Received 29 October 2002; accepted 13 January 2003) Supported by United States Department of Energy Grant No. DE-FG03-97ER544. Invited speaker. Paper BI2 3, Bull Am. Phys. Soc. 47, 21 (2002).
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-97ER54438
Subject Keywords:magnetic flux; plasma theory; plasma flow; plasma toroidal confinement
Issue or Number:5
Record Number:CaltechAUTHORS:BELpop03
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1892
Deposited By: Archive Administrator
Deposited On:22 Feb 2006
Last Modified:12 Dec 2019 17:06

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